Moderate Algebra Solved QuestionAptitude Discussion

 Q. On May 1, 2007, two organisations ($A$ and $B$) were formed with $n$ members each. On the first day of each subsequent month, $m$ members join $A$ while the number of members in $B$ gets multiplied by $p$. On September 2, 2007, both organisations have the same number of members. If $m = 20n$, find $p$?
 ✖ A. 2 ✔ B. 3 ✖ C. 4 ✖ D. 5

Solution:
Option(B) is correct

The number of members in $A$ on Oct 2, 2007:

$=n+4m=n+80n=81n$

Number of members in $B$ on Oct 2, 2007:

$=n×p×p×p×p$

As given in the question, now both organisations have the same number of members.

$⇒ 81n=n×p^4$

$⇒ p=3$

Note: As per the comment by Prabal the date mentioned in the question has been changed to September 2 from October 2.

(4) Comment(s)

Prabal
()

From May to October is 6 months, therefore the problem entails 6 terms of both series,

thus, the equation shall be $n+5m=np^5$, which shall obviously not give a valid answer. Thus, the date should be September 2nd not October 2nd.

Deepak
()

Thank you Prabal for pointing out the correction. Updated the question.

Anurag
()

Mistake in Question .. Guys .. Has to be Sep 2007 instead f Oct 2007 ..

Pranshu
()

it must be $n+5m=np^5$